Saturday, 11:10 - 12:50 - Room 146

*Stream: Linear and nonlinear optimization*

Chair:

- A unified modeling approach for computing (s, S) policies with stochastic demand

We present mixed integer linear programming (MILP) models to compute near optimal parameters for the nonstationary stochastic lot sizing problem under the (s, S) control policy. We discuss different variants of the stochastic lot sizing problem based on piecewise linearization of first order loss functions. Our MILP models favourably compare to existing methods: they are the first MILP heuristics to approximate (s, S) policy parameters, and they work for generically distributed demand patterns. Computational experiments demonstrate the effectiveness and versatility of our models.

- Generating the efficient frontier for a class of bicriteria generalized fractional programming

A bicriteria maximization problem is considered. The first component of the objective function is the ratio of powers of affine functions while the second one is linear. Under suitable assumptions the first criterium turns out to be pseudoconcave so that the connectedness of the efficient frontier is guaranteed. The theoretical properties of the problem allow to generate the whole efficient frontier by means of the solutions of suitable parametric scalar optimization problems. A solution method for generating the efficient frontier is proposed and validated by means of a computational test.

- Weak, strong and linear convergence of a double-layer fixed point algorithm

In this talk we consider consistent convex feasibility problems in a real Hilbert space defined by a finite family of sets Ci. In particular, we are interested in the case where Ci=Fix Ui=z: pi(z)=0, Ui is an operator and pi is a proximity function. Moreover, we assume that the computation of pi is at most as difficult as the evaluation of Ui and this is at most as difficult as projecting onto Ci. The considered double-layer fixed point algorithm applies certain outer and inner controls.

- The complexity of simple models - a study of worst and typical hard cases for the Standard Quadratic Optimization Problem

Despite simplicity of the StQP (minimize a quadratic over the standard simplex), nonconvex instances of StQPs allow for rich patterns of coexisting local solutions. We improve known lower bounds for the number of strict local solutions by constructing rare instances. Indeed, random instances have quite sparse solutions, and their expected numbers are considerably lower than in the worst case. Here we obtain an empirical sparsity distribution of strict local solutions to the StQP by systematically searching promising instances, refining average-case analysis of this NP-hard problem class.

- Convergence properties of the weak subgradient algorithm in nonconvex optimization

Weak subgradient based solution algorithm that does not require convexity conditions on neither the objective function nor the set of feasible solutions is introduced.At every iteration, to generate a new solution, the algorithm uses weak subgradients of the objective function at the point generated in the previous iteration. In this paper we introduce different step size parameters. Convergence properties of the presented algorithm are investigated for various step size parameters. The performance of the algorithm is demonstrated on test problems.